在增强器同步加速器中加速极化电子（正电子）束流时，可能因穿越众多自旋退极化共振而发生退极化，从而限制其应用。我们研究了环形正负电子对撞机（Circular Electron Positron Collider，CEPC）一个100 km量级增强器磁聚焦结构的自旋退极化共振结构。该磁聚焦结构具有8个弧区，包含数百个FODO单元，并与直线段交替排列，因此具有很高的周期性。分析表明，在120 GeV以上的超强共振附近，内禀自旋共振和非理想自旋共振对共振强度的贡献会相干叠加；而在较低束流能量下，这些贡献大多相互抵消，使共振强度总体较弱。详细模拟证实，在快速加速至45.6 GeV和80 GeV的过程中，束流极化基本可以保持，但在更高能量下可能出现严重退极化。本研究表明，在不借助Siberian snake（西伯利亚蛇）的情况下，将极化电子（正电子）束流加速到超高束流能量是可能的，并支持将高极化束流注入对撞机环，作为未来100 km量级环形e+e−对撞机开展共振退极化测量和纵向极化对撞束实验的有吸引力方案。
英文摘要：
Acceleration of polarized electron~(positron) beams in a booster synchrotron may suffer from depolarization due to crossings of many spin depolarization resonances, which could limit its applications. We have studied the spin depolarization resonance structure of a 100~km scale booster lattice of the Circular Electron Positron Collider~(CEPC). The lattice has 8 arc regions with hundreds of FODO cells, interleaved with straight sections, which leads to a high periodicity. Our analysis shows the contributions to the strength of intrinsic and imperfection spin resonances add up coherently near the super strong resonances beyond 120 GeV, but mostly cancel out and result in generally weak resonance strengths at lower beam energies. Detailed simulations confirm that beam polarization can be mostly maintained in the fast acceleration to 45.6 GeV and 80 GeV, but severe depolarization may occur at even higher energies. This study suggests the possibility of acceleration of polarized electron~(positron) beams to ultra-high beam energies without the help of Siberian snakes, and supports injecting highly polarized beams into the collider rings as an attractive solution for resonant depolarization measurements and longitudinal polarized colliding beam experiments for future 100~km scale circular e$^{+}$e$^{-}$ colliders.
The Future Circular Collider (FCC) study investigates the feasibility of circular colliders in the post-LHC era. The sub-study FCC-ee is a 100 km electron positron collider in the energy range of 90-365 GeV. In order to achieve a design luminosity in the order of $10^{36}$cm$^{-2}$s$^{-1}$ continuous top-up injection is required. The injector chain therefore includes a 100 km booster synchrotron in the same tunnel as the collider rings. This paper presents the lattice design of this booster synchrotron and the first dynamic aperture studies based on the chromaticity correction sextupole scheme…
The analytical expression of the magnetic field distribution within the aperture of a circular vacuum chamber due to the induced eddy is derived. Two cases are discussed, one is the absence of iron, the other is that the vacuum chamber is between the iron poles, that implies the use of the image current methods. The current angular distribution in the vacuum chamber can be calculated from the ramping rate of the exposed field, then the contour integration is applied to the circular current to obtain the field distribution. The formula can be used to estimate the undesired fields from a circula…
The beam aperture of a particle accelerator defines the clearance available for the circulating beams and is a parameter of paramount importance for the accelerator performance. At the CERN Large Hadron Collider (LHC), the knowledge and control of the available aperture is crucial because the nominal proton beams carry an energy of 362 MJ stored in a superconducting environment. Even a tiny fraction of beam losses could quench the superconducting magnets or cause severe material damage. Furthermore, in a circular collider, the performance in terms of peak luminosity depends to a large extent o…
The CERN FCC-ee top-up booster synchrotron will accelerate electrons and positrons from an injection energy of 20 GeV up to an extraction energy between 45.6 GeV and 182.5 GeV depending on the operation mode. These accelerated beams will be used for the initial filling of the high-luminosity FCC-ee collider and for keeping the beam current constant over time using continuous top-up injection. Due to the high-intensities of the circulating beams, collective effects may represent a limitation in the top-up booster. In this work we present a first evaluation of the impedance model and the effects…
In order to meet the needs of Fermilabs planned post-collider experimental program, the total proton throughput of the 8 GeV Booster accelerator must be nearly doubled within the next two years. A system of 48 ramped corrector magnets has recently been installed in the Booster to help improve efficiency and allow for higher beam intensity without exceeding safe radiation levels. We present the preliminary results of beta function measurements made using these corrector magnets. Our goal is to use the correctors to reduce irregularities in the beta function, and ultimately to introduce localize…
The Low Energy Relativistic Heavy Ion Collider (RHIC) electron Cooler (LEReC) is designed to deliver a 1.6 MeV to 2.6 MeV electron beam, with rms dp/p less than 5e-4. The superconducting radiofrequency (SRF) Booster Cavity is the major accelerating component in LEReC. It is a 0.4 cell cavity operating at 2 K, providing a maximum energy gain of 2.2 MeV. It is modified from an experimental Energy Recovery Linac (ERL) photocathode gun, and thus has fundamental power couplers (FPCs), pickup (PU) couplers (field probes) and HOM coupler close to each other on the same side of the cavity. Direct capa…
Updates on Impedance Studies for the FCC-ee High Energy Booster
GANIL；CEA（法国原子能和替代能源委员会）；CERN（欧洲核子研究组织）；IPM（伊朗数学物理研究所）；University of Rome La Sapienza（罗马大学）；INFN - Roma1（意大利国家核物理研究所罗马第一分部）；INFN - LNF（意大利国家核物理研究所弗朗卡蒂实验室）；University of Caen Normandy（诺曼底卡昂大学）；Paris-Saclay University（巴黎萨克雷大学）
The Circular Electron Positron Collider (CEPC) is a large international scientific project initiated and hosted by China. It is located in a 100-km circumference underground tunnel. The accelerator complex consists of a linear accelerator (Linac), a damping ring (DR), the Booster, the Collider and several transport lines. In the tunnel, space is reserved for a future pp collider, SPPC. The CEPC center-of-mass energy is 240 GeV, and at that collision energy will serve as a Higgs factory. The design also allows operation at 91 GeV for a Z factory and at 160 GeV for a W factory. The heart of the …
We review the different performance limitations of circular colliders, namely the limitations of energy reach, maximum attainable luminosity and beam lifetime. This paper considers only head-on collisions. We consider the range of beam energies from 45GeV to 250 GeV and collider circumferences from 20 to 100kms.
In this paper we showed a systematic method of appropriate parameter choice for a circular pp collider by using analytical expression of beam-beam tune shift limit started from given design goal and technical limitations. A parameter space has been explored. Based on parameters scan and considerations from RF systems, a set of appropriate parameter designed for a 50Km and a 100Km circular proton-proton collider was proposed.
Renewed interest in circular e+e- colliders has spurred designs of single beam-pipe machines, like the CEPC in China, and double beam pipe ones, such as the FCC-ee effort at CERN. Single beam-pipe designs profit from lower costs but are limited by the number of bunches that can be accommodated in the machine. We analyse these performance limitations and propose a solution that can accommodate O(1000) bunches while keeping more than 90% of the ring with a single beam pipe.
Several proposals exist for future circular electron-positron colliders designed for precise measurements of the Higgs boson characteristics and electroweak processes. At very high energies, synchrotron radiation of the particles in a strong electromagnetic field of the oncoming bunch (beamstrahlung) becomes extremely important, because of degradation of the beam lifetime and luminosity. We present theoretical calculations of beamstrahlung (including the beam lifetime reduction and the energy spread increase) which are benchmarked against quasi strong-strong computer simulation. Calculation re…
The design of future circular high-energy hadron colliders is based on the achievement of challenging magnetic fields, needed to keep the hadron beams orbiting along the ring circumference. The strength of the dipolar magnetic field is a function of the machine radius, beam energy, and of the fraction of the ring circumference that can be filled with dipoles. In this paper we propose to use a combined-function periodic cell to maximise the filling factor of the dipole magnets. The optical properties of the proposed periodic structure are discussed in detail together with the design of the supe…
The use of resonant depolarization has been suggested for precise beam energy measurements (better than 100 keV) in the $e^{+}e^{-}$ Future Circular Collider (FCC-$e^{+}e^{-}$) for Z and WW physics at 45 and 80 GeV beam energy respectively. Longitudinal beam polarization would benefit the Z peak physics program; however it is not essential and therefore it will be not investigated here. In this paper the possibility of self-polarized leptons is considered. Preliminary results of simulations in presence of quadrupole misalignments and beam position monitors (BPMs) errors for a simplified FCC-$e…
A proof-of-principle experimental setup for the extraction of 6 GeV electrons from the DESY II Booster Synchrotron using the channeling effect in a bent crystal is elaborated. Various aspects of the experimental setup were investigated in detail, such as the particle beam dynamics during the extraction process, the manufacturing and characterization of bent crystals, and the detection of the extracted beam. In order to optimize the crystal geometry, the overall process of beam extraction was simulated, taking into account the influence of radiation energy losses. As result it is concluded that…
The robust conjugate direction search (RCDS) method has high tolerance to noise in beam experiments. It has been demonstrated that this method can be used to optimize the machine performance of a light source online. In our study, taking BEPCII as an example, the feasibility of online tuning of the luminosity in a circular collider is explored, through numerical simulation and preliminary online experiments. It is shown that the luminosity that is artificially decreased by a deviation of beam orbital offset from optimal trajectory can be recovered with this method.
Physically speaking, the delta function like beam-beam nonlinear forces at interaction points (IPs) act as a sum of delta function nonlinear multipoles. By applying the general theory established in ref. 1, in this paper we investigate analytically the beam-beam interaction limited dynamic apertures and the corresponding beam lifetimes for both the round and the flat beams. Relations between the beam-beam limited beam lifetimes and the beam-beam tune shifts are established, which show clearly why experimentally one has always a maximum beam-beam tune shift, ξ_{y, max}, around 0.045 for e-^+e$^…
The Future Circular Collider (FCC) study was launched as a world-wide international collaboration hosted by CERN. Its goal is to push the field to the next energy frontier beyond LHC, increasing by an order of magnitude the mass of particles that could be directly produced, and decreasing by an order of magnitude the subatomic distances to be studied. The FCC study covers two accelerators, namely, an energy-frontier hadron collider (FCC-hh) and a highest luminosity, high-energy lepton collider (FCC-ee). Both rings are hosted in the same 100 km tunnel infrastructure, replicating the CERN strate…
The FCC-ee is a proposed future high-energy, high-intensity and high-precision lepton collider. Here, we present the latest development for the FCC-ee interaction regions, which shall ensure optimum conditions for the particle physics experiments. We discuss measures of background reduction and a revised interaction region layout including a low impedance compact beam chamber design. We also discuss the possible impact of the radiation generated in the interaction region including beamstrahlung.
The recent discovery of a light Higgs boson has opened up considerable interest in circular e+e- Higgs factories around the world. We report on the progress of the TLEP concept since last year. TLEP is an e+e- circular collider capable of very high luminosities in a wide centre-of-mass (ECM) spectrum from 90 to 350 GeV. TLEP could be housed in a new 80 to 100 km tunnel in the Geneva region. The design can be adapted to different ring circumference (e.g. LEP3 in the 27 km LHC tunnel). TLEP is an ideal complementary machine to the LHC thanks to high luminosity, exquisite determination of ECM and…
The quite low Higgs particle mass makes it natural for the next high energy facility to be a circular e+e- Higgs factory and, after that, a next-generation p,p collider in the same tunnel. Surveying the luminosity-limiting phenomena of synchrotron radiation power loss, beam-beam interaction limitations, and beamstrahlung, scaling laws are established that fix all parameters of the Higgs factory, as functions of assumed radius $r$, and RF power $P$. at least to a first approximation. Historically the accelerator formalisms of electron and hadron rings have been distinguished largely by the impo…
Building on the Renormalization Group (RG) method the beam-beam interaction in circular colliders is studied. A regularized symplectic RG beam-beam map, that describes successfully the long-time asymptotic behavior of the original system has been obtained. The integral of motion possessed by the regularized RG map has been used to construct the invariant phase space density (stationary distribution function), and a coupled set of nonlinear integral equations for the distributions of the two colliding beams has been derived.
This paper is a summary report of the ICFA Beam Dynamics Workshop 'Accelerators for a Higgs Factory: Linear vs. Circular' (HF2012). It discusses four types of accelerators as possible candidates for a Higgs factory: linear e+e- colliders, circular e+e- colliders, muon collider and photon colliders. The comparison includes: physics reach, performance (energy and luminosity), upgrade potential, technology maturity and readiness, and technical challenges requiring further R&D.
The FCC-ee impedance model is being constantly updated closely following the vacuum chamber design and parameters evolution. In particular, at present, a thicker NEG coating of 150 nm (instead of previous 100 nm) has been suggested by the vacuum experts, and a more realistic impedance model of the bellows has been investigated. Moreover, also the transverse impedance has been updated by considering the same sources as for the longitudinal case. Therefore, the FCC-ee impedance database is getting more complete and the impedance model is being refined. In this paper we describe the presently ava…
We discuss the goals, the designs, the state of technical readiness, and the critical R&D needs of the accelerators that are currently under discussion as Higgs and electroweak factories. We also address the respective staging options enabling future energy-frontier colliders. The accelerators covered are based on many different techniques and approaches. They include several circular colliders, various linear colliders, colliders based on energy recovery linacs (ERLs), ERL-ring combinations, as well as gamma-gamma colliders. The linear colliders proposed consist of options for the Internation…
We study the phenomena of spin rotation and depolarization of high-energy particles in crystals in the range of high energies that will be available at Hadron Collider (LHC) and Future Circular Collider (FCC). It is shown that these phenomena can be used to measure the anomalous magnetic moments of short-lived particles in this range of energies. We also demonstrate that the phenomenon of particle spin depolarization in crystals provides a unique possibility of measuring the anomalous magnetic moment of negatively-charged particles (e.g., beauty baryons), for which the channeling effect is ham…
After the discovery of the Higgs boson at the Large Hadron Collider in 2012, several possible future circular colliders -- Higgs factories are proposed, such as FCC-ee and CEPC. At these highest-energy $e^+e^-$ colliders, beamstrahlung, namely the synchrotron radiation emitted in the field of the opposing beam, can greatly affect the equilibrium bunch length and energy spread. If the dispersion function at the collision point is not zero, beamstrahlung will also increase the transverse emittances. In this letter, we first show that, for circular Higgs factories, a classical description of the …
Various methods of obtaining longitudinally polarized positrons for future linear colliders are reviewed. Special attention is paid to the schemes using circularly polarized high-energy photons for positron production. Most effectively such photons are obtained from electrons passing through a helical undulator or colliding with a circularly polarized laser wave. Spectrum and polarization of radiation emitted during helical motion of electrons are considered in detail. A new simple presentation of known formulas is used to account for the influence of the wave intensity, of the electron-beam a…
It is proposed to place the arcs of an SLC-type facility inside the tunnel of a Future Circular Collider (FCC). Accelerated by a linear accelerator (linac), electron and positron beams would traverse the bending arcs in opposite directions and collide at centre-of-mass energies considerably exceeding those attainable at circular $e^{+}e^{-}$ colliders. The proposed SLC-type facility would have the same luminosity as a conventional two-linac $e^{+}e^{-}$ collider. Using an optical free-electron laser, the facility could be converted into a $γγ$ collider. A superconducting L-band linac at the pr…
As the only high-temperature superconducting (HTS) material available as an isotropic, twisted, multifilamentary round wire, Bi-2212 is very promising for expanding the high-field superconducting accelerator magnet toolbox beyond the round-wire, isotropic Nb-Ti and Nb3Sn conductors used by HEP so far. In this paper, we describe the important roles that Bi-2212 might play for future high energy circular colliders including both high energy proton and muon colliders. We describe its present technology status (conductor development, magnet design concepts, prototype magnet status) and then provid…
We present a Circular Energy Recovery Collider (CERC) as an alternative approach for a high-energy high-luminosity electron-positron collider to current designs for high-energy electron-positron colliders either based on two storage rings with 100 km circumference or two large linear accelerators. Using Energy Recovery Linacs (ERL) located in the same-size 100 km tunnel would allow a large reduction of the beam energy losses, and therefore a reduction of the power consumption, while providing higher luminosity. It also opens a path for extending the center-of-mass (CM) energy to 500 GeV, which…
The completion of the Standard Model of particle physics by the discovery of a light Higgs boson at the LHC in 2012 triggered the debate about the best way forward to discover physics beyond the Standard Model. At the eve of the update of the European Strategy of particle physics, this article summarises the motivation and status of the different collider projects in particle physics at the energy frontier. This article reflects the status as of December 2018 and the reader is invited to follow closely updated information of the presented projects.
In this paper we present alternative approach for Future Circular electron-positron Collider. Current 100 km circumference design with the top CM energy of 365 GeV (182.5 GeV beam energy) is based on two storage rings to circulate colliding beams. One of the ring-ring design shortcomings is enormous power consumption needed to compensate for 100 MW of the beam energy losses for synchrotron radiation. We propose to use energy recovery linac located in the same tunnel to mitigate this drawback. We show in this paper that our approach would allow a significant, up to an order of magnitude, reduct…
The worldwide High Energy Physics community widely agrees that the next collider should be a Higgs factory. Acknowledging this priority, in 2021 CERN has launched the international Future Circular Collider (FCC) Feasibility Study (FS). The FCC Integrated Project foresees, in a first stage, a high-luminosity high-energy electron-positron collider, serving as Higgs, top and electroweak factory, and, in a second stage, an energy frontier hadron collider, with a centre-of-mass energy of at least 100 TeV. In this paper, we address a few key elements of the FCC-ee accelerator design, its performance…
The hadron collider studied in the Future Circular Collider (FCC) project could operate with protons and lead ions in similar operation modes as the LHC. In this paper the potential performances in lead-lead, proton-lead and proton-proton collisions are investigated. Based on average lattice parameters, the strengths of intra-beam scattering and radiation damping are evaluated and their effect on the beam and luminosity evolution is presented. Estimates for the integrated luminosity per fill and per run are given, depending on the turnaround time. Moreover, the beam-beam tune shift and bound f…
In this White Paper for the Snowmass 2021 Process, we propose the establishment of a magnet Leading-Edge technology And Feasibility-directed Program (LEAF Program) to achieve readiness for a future collider decision on the timescale of the next decade. The LEAF Program would rely on, and be synergetic with, generic R&D efforts presently covered - in the US - by the Magnet Development Program (MDP), the Conductor Procurement and R&D (CPRD) Program and other activities in the Office of HEP supported by Early Career Awards (ECA) or Lab Directed R&D (LDRD) funds. Where possible, ties to synergetic…
This note describes two versatile accelerator complexes that could be built at a Future Circular Collider (FCC) in order to produce $e^{+}e^{-}$, $γγ$ and $ep$ collisions. The first facility is an SLC-type machine comprising a superconducting L-band linear accelerator (linac) and two arcs of bending magnets inside the FCC tunnel. Accelerated by the linac, electron and positron beams would traverse the arcs in opposite directions and collide at centre-of-mass energies considerably exceeding those attainable at circular $e^{+}e^{-}$ colliders. The proposed SLC-type facility would have the same l…
X-ray reflection: a FLUKA model and its application in the design of synchrotron light beamlines and CERN's Future Circular Collider
European Organization for Nuclear Research（欧洲核子研究组织）；Facultat de Física, Universitat de Barcelona（巴塞罗那大学物理学院）；Argonne National Laboratory（阿贡国家实验室）；University of Liverpool（利物浦大学）；ALBA Synchrotron（阿尔巴同步辐射中心）；European Synchrotron Radiation Facility（欧洲同步辐射装置）；Reflective X-ray Optics LLC（反射X射线光学有限责任公司）
The international Future Circular Collider (FCC) study aims at a design of $pp$, $e^+e^-$, $ep$ colliders to be built in a new 100 km tunnel in the Geneva region. The $e^+e^-$ collider (FCC-ee) has a centre of mass energy range between 90 (Z-pole) and 375 GeV (tt_bar). To reach such unprecedented energies and luminosities, the design of the interaction region is crucial. The crab-waist collision scheme has been chosen for the design and it will be compatible with all beam energies. In this paper we will describe the machine detector interface layout including the solenoid compensation scheme. …
A beam optics scheme has been designed for the Future Circular Collider-e+e- (FCC-ee). The main characteristics of the design are: beam energy 45 to 175 GeV, 100 km circumference with two interaction points (IPs) per ring, horizontal crossing angle of 30 mrad at the IP and the crab-waist scheme [1] with local chromaticity correction. The crab-waist scheme is implemented within the local chromaticity correction system without additional sextupoles, by reducing the strength of one of the two sextupoles for vertical chromatic correction at each side of the IP. So-called "tapering" of the magnets …
Now that the mass of the Higgs boson is known, circular electron positron colliders, able to measure the properties of these particles with high accuracy, are receiving considerable attention. Design studies have been launched (i) at CERN with the Future Circular Colliders (FCC), of which an e+e- collider is a potential first step (FCC-ee, formerly caller TLEP) and (ii) in China with the Circular Electron Positron Collider (CEPC). Hosted in a tunnel of at least 50 km (CEPC) or 80-100 km (FCC), both projects can deliver very high luminosity from the Z peak to HZ threshold (CEPC) and even to the…
The Future Circular Collider (FCC) study aims at designing different options of a post-LHC collider. The high luminosity electron-positron collider FCC-ee based on the crab waist concept is considered as an intermediate step on the way towards FCC-hh, a 100 TeV hadron collider using the same tunnel of about 100 km. Due to a high intensity of circulating beams the impact of collective effects on FCC-ee performance has to be carefully analyzed. In this paper we evaluate beam coupling impedance of the FCC-ee vacuum chamber, estimate thresholds and rise times of eventual single- and multibunch bea…
In particle accelerators, pumping holes in a vacuum chamber can be a source of unwanted broadband coupling impedance, leading to beam instabilities. Analytical methods have been previously developed to estimate the impedance of holes in circular-like chambers e.g. the beamscreen of the Large Hadron Collider (LHC). More sophisticated chamber designs like that of the High Energy LHC (HE-LHC) and the Future Circular Collider (FCC-hh) call for a different way to calculate the impedance. We propose using decomposition of the wakefield into synchronous traveling waves and employing a numerical solve…
High energy particle colliders have been in the forefront of particle physics for more than three decades. At present the near term US, European and international strategies of the particle physics community are centered on full exploitation of the physics potential of the Large Hadron Collider (LHC) through its high-luminosity upgrade (HL-LHC). A number of next generation collider facilities have been proposed and are currently under consideration for the medium- and far-future of the accelerator-based high energy physics. In this paper we offer a uniform approach to evaluation of various acc…
Discoveries at high-energy particle colliders have established the standard model of particle physics. Technological innovation has helped to increase the collider energy at a much faster pace than the corresponding costs. New concepts will allow reaching ever higher luminosities and energies throughout the coming century. Cost-effective strategies for the collider implementation include staging. For example, a future circular collider could first provide electron-positron collisions, then hadron collisions (proton-proton and heavy-ion), and finally the collision of muons. Cooling-free muon co…
Multi-TeV center of mass energy ep colliders based on the Future Circular Collider (FCC) and linear colliders (LC) are proposed and corresponding luminosity values are estimated. Parameters of upgraded versions of the FCC are determined to optimize luminosity of electron-proton collisions keeping beam-beam effects in mind. It is shown that L_{ep}\sim10^{32}\,cm^{-2}s^{-1} can be achieved with moderate upgrade of the FCC parameters.
Construction of future electron-positron colliders (or dedicated electron linac) and muon colliders close to Future Circular Collider will give opportunity to utilize highest energy proton and nucleus beams for lepton-hadron and photon-hadron collisions. In this paper we estimate main parameters of the FCC based ep and μp colliders.
Following the discovery of the Higgs boson at LHC, new large colliders are being studied by the international high-energy community to explore Higgs physics in detail and new physics beyond the Standard Model. In China, a two-stage circular collider project CEPC-SPPC is proposed, with the first stage CEPC (Circular Electron Positron Collier, a so-called Higgs factory) focused on Higgs physics, and the second stage SPPC (Super Proton-Proton Collider) focused on new physics beyond the Standard Model. This paper discusses this second stage.
